Circuits, Systems and Signal Processing

, Volume 13, Issue 1, pp 77–97 | Cite as

Design of FIR digital filters with flatness constraints for the error function

  • Rudolf Rabenstein


A method will be presented for the approximation of a desired frequency response by the frequency response of a FIR filter. It is possible to match the functional values and an arbitrary number of derivatives of both responses for zero frequency, thus making the error flat up to a desired degree. Remaining degrees of freedom are used for a weightedL2-approximation. Closed form design formulae will be given.


Frequency Response Closed Form Error Function Arbitrary Number Digital Filter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P. Steffen, Fourier-approximation with interpolative constraints,AEÜ, Band 38, Heft 6, (1984), 363–367.Google Scholar
  2. [2]
    H. W. Schuessler and P. Steffen, An approach for designing systems with prescribed behavior at distinct frequencies regarding additional constraints, Proceedings of the ICASSP 1985, Tampa, USA, 61–64.Google Scholar
  3. [3]
    P. Steffen, On digital smoothing filters: a brief review of closed form solutions and two new filter approaches,Circuits, Systems, Signal Processing,5 (2), (1986), 187–210.Google Scholar
  4. [4]
    H. W. Schuessler and P. Steffen, Some Topics in Advanced Filter Design, inAdvanced Topics in Signal Processing, J. S. Lim and A. V. Oppenheim, (eds). Prentice Hall, Englewood Cliffs, 1988.Google Scholar
  5. [5]
    R. W. Hamming,Numerical Methods for Scientists and Engineers, McGraw-Hill, New York, 1973.Google Scholar
  6. [6]
    P. Steffen, private communication.Google Scholar
  7. [7]
    R. Rabenstein, Design of FIR Digital Filters with Prescribed Derivatives at Zero Frequency, Proceedings 1989 URSI International Symposium on Signals, Systems and Electronics, Erlangen, Germany, 705–708.Google Scholar
  8. [8]
    R. Rabenstein, Diskrete Simulation linearer mehrdimensionaler kontinuierlicher System, (Discrete Simulation of Linear Multidimensional Continuous Systems), Dissertation, Erlangen, Germany, 1991 (in German).Google Scholar
  9. [9]
    R. Rabenstein, Stimulation of linear continuous systems with distributed parameters, Simulation Practice and Theory, 1993, in press.Google Scholar

Copyright information

© Birkhäuser 1994

Authors and Affiliations

  • Rudolf Rabenstein
    • 1
  1. 1.Lehrstuhl für NachrichtentechnikUniversität Erlangen-NürnbergErlangenGermany

Personalised recommendations